Science:Math Exam Resources/Courses/MATH307/April 2013/Question Section 202 07 (e)/Solution 1

The equations are:

${\begin{aligned}d_{1}&=1\\a_{1}+b_{1}+c_{1}+d_{1}&=0\\d_{2}&=0\\a_{2}+b_{2}+c_{2}+d_{2}&=2\\3a_{1}+2b_{1}+c_{1}-c_{2}&=0\\2b_{1}&=0\\6a_{2}+2b_{2}&=0\\6a_{1}+2b_{1}-2b_{2}&=0\end{aligned}}$

${\begin{bmatrix}0&0&0&1&0&0&0&0\\1&1&1&1&0&0&0&0\\0&0&0&0&0&0&0&1\\0&0&0&0&1&1&1&1\\3&2&1&0&0&0&-1&0\\0&2&0&0&0&0&0&0\\0&0&0&0&6&2&0&0\\6&2&0&0&0&-2&0&0\end{bmatrix}}{\begin{bmatrix}a_{1}\\b_{1}\\c_{1}\\d_{1}\\a_{2}\\b_{2}\\c_{2}\\d_{2}\\\end{bmatrix}}={\begin{bmatrix}1\\0\\0\\2\\0\\0\\0\\0\\\end{bmatrix}}$

Matlab:

   A=[0,0,0,1,0,0,0,0; 1,1,1,1,0,0,0,0; 0,0,0,0,0,0,0,1; ...
      0,0,0,0,1,1,1,1; 3,2,1,0,0,0,-1,0; 0,2,0,0,0,0,0,0; ...
      0,0,0,0,6,2,0,0; 6,2,0,0,0,-2,0,0];
   b=[1,0,0,2,0,0,0,0]’;
   a=A\b;